Consider the following three European call options, all with expiration at time T = 1: option A has strike $10; option B has strike $15; and option C has strike $20

Suppose that the premium of the three options are $7, $3, $1 for A, B, and C, respectively, today (time 0). Suppose the price on the stock today is $14.

(b) Suppose the risk-free rate is constant at 0%. Graph the profit function for each of the previous strategies.

(c) Suppose the risk-free rate is constant at 5%. Graph the profit function for the butterfly strategy at time T taking into consideration the time value of the initial cost. By how much would the asset have to change over the year for your butterfly portfolio to be a loss?